Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Quasigauge Spaces with Generalized Quasipseudodistances and Periodic Points of Dissipative Set-Valued Dynamic Systems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 712706 22 pages doi 2011 712706 Research Article Quasigauge Spaces with Generalized Quasipseudodistances and Periodic Points of Dissipative Set-Valued Dynamic Systems Kazimierz WIodarczyk and Robert Plebaniak Department of Nonlinear Analysis Faculty of Mathematics and Computer Science University of Udi Banacha 22 90-238 Lodz Poland Correspondence should be addressed to Kazimierz Wlodarczyk wlkzxa@ Received 13 September 2010 Revised 19 October 2010 Accepted 10 November 2010 Academic Editor Jen Chih Yao Copyright 2011 K. Wlodarczyk and R. Plebaniak. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. In quasigauge spaces we introduce the families of generalized quasipseudodistances and we define three kinds of dissipative set-valued dynamic systems with these families of generalized quasi-pseudodistances and with some families of not necessarily lower semicontinuous entropies and next assuming that quasigauge spaces are left K sequentially complete but not necessarily Hausdorff we prove that for each starting point each dynamic process or generalized sequence of iterations of these dissipative set-valued dynamic systems left converges and we also show that if an iterate of these dissipative set-valued dynamic systems is left quasiclosed then these limit points are periodic points. Examples illustrating ideas methods definitions and results are constructed. 1. Introduction The study of quasigauge spaces initiated by Reilly 1 has a long history. These spaces generalize topological spaces quasiuniform spaces and quasimetric spaces. Studies of asymmetric structures in these spaces and their applications to problems in theoretical computer science are important. There exists an extensive literature .
